The question asks to count functions between finite sets satisfying properties such as monotonicity, surjectivity, equal-sized preimages, or conditions on compositions.
Q70. Let $A = \{ 1,3,7,9,11 \}$ and $B = \{ 2,4,5,7,8,10,12 \}$. Then the total number of one-one maps $f : \mathrm { A } \rightarrow \mathrm { B }$, such that $f ( 1 ) + f ( 3 ) = 14$, is : (1) 480 (2) 240 (3) 120 (4) 180